Marc Honikel
7)%.%2"!3%$ ).4%2&%2/-%42)# 3)'.!452% 2%#/.3425#4)/.
-ARC (/.)+%,
&EDERAL )NSTITUTE OF 4ECHNOLOGY :URICH 3WITZERLAND
)NSTITUTE FOR 'EODESY AND 0HOTOGRAMMETRY
MARCHONIKEL GEODBAUGETHZCH
7ORKING 'ROUP ))
+%9 7/2$3 )NTERFEROMETRY $%- 3IMULATION 2ECONSTRUCTION $ATA &USION
!"342!#4
!FTER ALMOST TEN YEARS OF REGULAR SPACEBORNE 3!2 DATA SUPPLY VARIOUS MICROWAVE REMOTE SENSING TECHNIQUES ARE
ESTABLISHED TODAY !MONG THEM 3!2 INTERFEROMETRY )N3!2 AND ITS APPLICATIONS LIKE DIGITAL ELEVATION MODEL $%-
GENERATION OR SURFACE CHANGE DETECTION MAY BE THE MOST EXCITING ONES WHICH THE RECENT SHUTTLE RADAR TOPOGRAPHY
MISSION 324- HAS PROVED IMPRESSIVELY 3!2 INTERFEROMETRY TAKES ADVANTAGE FROM THE PHASE SIGNAL PROPERTIES AND IS
USED TO DERIVE THE TOPOGRAPHIC HEIGHT OF AN IMAGE PIXEL 4HE INTERFEROMETRIC PHASE IE THE PHASE DIFFERENCE BETWEEN
TWO SENSOR POSITIONS AND THE TARGET IS A MEASURE FOR THE TRAVEL PATH LENGTH DIFFERENCE OF THE 3!2 WAVES PROPORTIONAL TO
THE TARGET HEIGHT .EVERTHELESS SOME 3!2 SYSTEM INHERENT LIMITATIONS CORRUPT THESE MEASUREMENTS AND LEAVE AREAS
INACCESSIBLE FOR THE INTERFEROMETRIC EXAMINATION LIMITING THE USE OF INTERFEROMETRY ESPECIALLY IN STEEP TERRAIN 4HIS PAPER
ADDRESSES THE RECONSTRUCTION OF THE INTERFEROMETRIC SIGNATURE WITH A NEW APPROACH BASED ON THE 7IENER SIGNAL RESTORATION
PRINCIPLE WHICH DISTINGUISHES BETWEEN MORE AND LESS NOISE AFFECTED INTERFEROMETRIC PHASE VALUES THUS CONSIDERING THE
PARTIALLY EXTREME SIGNALTONOISE 3.2 DIFFERENCES WITHIN AN INTERFEROGRAM 4HE INTERFEROMETRIC PHASE IS ESTIMATED WITH
HELP OF A SYNTHETIC INTERFEROGRAM DERIVED FROM A STEREOOPTICAL $%- WHICH SERVES AS A COMPLEMENTARY DATA SOURCE )N
THIS WAY AN ESTIMATE OF THE PHASE IS RETRIEVED EVEN IN REGIONS OF LOW SIGNAL TO NOISE RATIO WHICH IN TURN IMPROVES THE
QUALITY OF THE )N3!2 $%- MEASUREMENT
4HE PROCEDURE IS APPLIED TO AN INTERFEROGRAM DERIVED FROM AN %23 IMAGE PAIR AND A PHOTOGRAMMETRIC $%- FROM
30/4 DATA !LL TREATED PHASE DEGRADATIONS HAVE BEEN REMOVED ENABLING PRECISE $%- GENERATION 4HE RESULTING $%SURPASSED BY FAR THE INITIAL STEREOOPTICAL AND )N3!2 $%-S IN COMPLETENESS AND ACCURACY THUS PROVING THE POWER OF
THE PROPOSED TECHNIQUE
).42/$5#4)/.
"Y MAPPING ABOUT OF THE LANDMASS OF THE WORLD INTERFEROMETRICALLY THE SUCCESSFUL SHUTTLE RADAR TOPOGRAPHY
MISSION WILL HELP SPREADING )N3!2 $%- DATA INTO MIDSCALE DATABASES )N ORDER TO DERIVE THE HEIGHT OF A POINT FROM THE
INTERFEROMETRIC PHASE MEASUREMENTS THE PHASE AMBIGUITIES COMING FROM THE π MEASUREMENT INTERVAL MUST FIRST BE
SOLVED WITH THE SOCALLED PHASE UNWRAPPING ADDING THE CORRECT MULTIPLE OF π TO EACH PHASE VALUE 0HASE UNWRAPPING
BECOMES EXTREMELY DIFFICULT IN CASES OF LOW 3.2 DUE TO SIGNAL DECORRELATION !LTHOUGH SINGLEPASS PHASE
MEASUREMENTS DO NOT SUFFER FROM TEMPORAL DECORRELATION OF THE PHASES WHICH RESTRICTS MASSIVELY THE USE OF )N3!2
HEIGHT MEASUREMENTS FROM SPACEBORNE REPEATPASS SYSTEMS THE SYSTEM INHERENT MEASUREMENT LIMITATIONS REMAIN
)N3!2 HEIGHT MEASUREMENTS ARE RESTRICTED TO TERRAIN NOT STEEPER THAN THE VIEWING ANGLE OF THE SENSOR LEAVING
MOUNTAINOUS REGIONS INACCESSIBLE FOR INTERFEROMETRIC ANALYSIS )N ADDITION TO THE TERRAIN INCLINATION THE SIGNAL
INTERACTION WITH CERTAIN TYPES OF VEGETATION CAUSING MULTIPLE SCATTERING OR PHASE JUMPS AFFECT THE MEASUREMENTS LOCALLY
AND ACT AS AN ADDITIONAL LOCAL NOISE SOURCE
)N3!2 HEIGHT INFORMATION MAY SERVE FOR THE ENHANCEMENT OF EXISTING $%- DATABASES UP TO NOW CONSISTING MAINLY OF
PHOTOGRAMMETRICALLY DERIVED $%-S 4HROUGH ITS GENERATION PROCESS POINT MATCHING AND FOLLOWING INTERPOLATION
STEREOOPTICAL $%- QUALITY IS LESS TERRAIN DEPENDENT THAN ITS 3!2 COUNTERPART /N THE OTHER HAND STEREOOPTICAL $%GENERATION ALSO SUFFERS FROM SYSTEM LIMITATIONS LIKE CLOUD OCCLUSIONS OR TEXTURE DEPENDENCY OF THE MATCHING PROCESS
RESULTING IN MEASUREMENT HOLES
"ECAUSE OF THE DIFFERENT DATA AND GENERATION PRINCIPLES THE HEIGHT MEASUREMENTS OF BOTH $%- SOURCES CAN BE ASSUMED
TO BE UNCORRELATED 4HEREFORE WHEN INTRODUCED THE GENERATION PROCESS OF THEIR COUNTERPART THE DATA WILL ENHANCE THE
INFORMATION CONTENT OF A SCENE 4HE FOLLOWING SECTIONS DEAL WITH THE POSSIBILITY OF OVERCOMING THE )N3!2 LIMITATIONS BY
FUSING )N3!2 WITH A STEREOOPTICAL $%- DATA WHICH ARE USED COMPLEMENTARILY TO THE 3!2 MEASUREMENTS
4HE COMPLEMENTARITY OF BOTH OPTICAL AND 3!2 HEIGHT MEASUREMENTS HAS ALREADY BEEN USED FOR DIFFERENT FUSION
APPROACHES FOR THE IMPROVEMENT OF $%-S FROM REMOTE SENSING DATA (ONIKEL )N ONE CASE OPTICAL HEIGHT
148
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
Marc Honikel
MEASUREMENTS SERVED AS AN APPROXIMATION OF THE MEAN TERRAIN SHAPE WHILE DETAILS FROM THE INTERFEROMETRIC $%- WERE
ADDED )N THE OTHER CASE WEIGHTS HAVE BEEN INTRODUCED TO THE FUSION PROCESS WHICH INDICATED THE LOCAL HEIGHT ERROR )N
BOTH CASES THE HEIGHT ERROR DECREASED SIGNIFICANTLY AFTER THE FUSION
4HE 7IENERBASED METHOD WHICH IS PROPOSED IN THIS PAPER UNIFIES THESE APPROACHES FOR THE PROCESSING OF
INTERFEROMETRIC PHASE MEASUREMENTS 4HE DATA ARE FUSED BY TAKING ADVANTAGE FROM HAVING A GENERAL APPROXIMATION FROM
AN INDEPENDENT DATA SOURCE AND KNOWLEDGE OF THE EXPECTED ERROR OF EACH MEASUREMENT 7ITH THE GREAT DEAL OF
INFORMATION AVAILABLE THROUGH THE INTRODUCTION OF THE SIMULATED INTERFEROGRAM THE FILTER IS REALIZED BY MODELING THE IDEAL
PHASE COURSE AND THEN FITTING THE MODEL TO THE OBSERVATION )T IS INTENDED TO IMPROVE THE INTERFEROMETRIC HEIGHT
DETERMINATION PROCESS BY RESTORATION OF THE NOISECORRUPTED INTERFEROMETRIC PHASE MEASUREMENTS THUS EASING THE NOISE
SENSITIVE PHASE UNWRAPPING PROCESS AND TAKING FULL ADVANTAGE OF THE )N3!2 HEIGHT ACCURACY WHICH IS THEORETICALLY
LIMITED BY THE 3!2 WAVELENGTH CMSCALE
7)%.%2 0(!3% %34)-!4)/.
4HE REDUCTION OF THE PHASE NOISE IS CRUCIAL FOR THE CORRECT DETERMINATION OF THE MULTIPLE π WHICH HAS TO BE ADDED TO
EACH PHASE VALUE DURING THE UNWRAPPING PROCESS )N PRESENCE OF NOISE PHASE JUMPS RESIDUALS CAN OCCUR WHICH SPOIL
THE IMPLICIT UNWRAPPING ASSUMPTION OF A SMOOTH TERRAIN WITH PHASE CHANGES NOT HIGHER THAN π BETWEEN TWO ADJACENT
VALUES 4HE UNWRAPPING IS BOUND TO FAIL IF THESE MEASUREMENTS ARE NOT EXCLUDED FROM THE PROCEDURE #OMMON
AUTOMATED PHASE UNWRAPPING TECHNIQUES EG USING GHOSTLINES 'OLDSTEIN ARE ABLE TO DEAL WITH THIS PROBLEM
ONLY TO A CERTAIN EXTENT ,ARGE REGIONS OF LOW 3.2 STILL LEAD EITHER TO FAILURE OF THE $%- GENERATION PROCESS OR WORSE
ADD A GLOBAL ERROR ALSO TO UNCORRUPTED PHASE MEASUREMENTS IF UNWRAPPED ERRONEOUSLY :EBKER GIVES AN
EVALUATION OF )N3!2 ERRORS AND TOPOGRAPHIC MAP ACCURACY FOR %23
#OMMON APPROACHES OF NOISE REDUCTION INCLUDE MULTILOOK IMAGE PROCESSING AVERAGING OR INTERFEROGRAM FILTERING !LL
THESE TECHNIQUES HAVE IN COMMON THAT THEY ARE HARDLY NOISE ADAPTIVE THUS AFFECTING ALSO VALID MEASUREMENTS WHILE
DEALING WITH THE NOISE 4HE PHASE RECONSTRUCTION IN REGIONS WHERE THE INTERFEROMETRIC MEASUREMENT FAILS EG DUE TO
LAYOVER IS GENERALLY NOT POSSIBLE WITH THESE METHODS 4HE PROPOSED METHOD AIMS THEREFORE AT A RESTORATION PROCESS
WHICH NOT ONLY REMOVES OR REDUCES THE NOISE BUT ALSO RESTORES THESE REGIONS WHERE THE PHASE MEASUREMENT PREVIOUSLY
FAILED
)NTERFEROMETRIC PHASE RESTORATION MODEL
4HE FOLLOWING CONSIDERATIONS RELATE TO THE GENERAL DEGRADATION AND RESTORATION MODEL GIVEN IN &IG IN WHICH THE
IMAGE VECTOR F IS SUBJECT TO SOME UNSPECIFIED TYPE OF DEGRADATION WHICH AFFECTS THE IMAGE BOTH SPATIALLY
MULTIPLICATIVELY RESULTING IN A BLURRED IMAGE GB AND POINTWISE ADDITIVELY RESULTING IN AN OBSERVATION G
!PPLIED TO THE INTERFEROMETRIC PHASE DEGRADATION CAUSES BOTH A LOCAL BLURRING OF THE FRINGE LINES AND ADDS TO THE LOCAL
NOISE %SPECIALLY BLURRING OF THE FRINGE LINES ENDANGERS CORRECT PHASE UNWRAPPING AS THE BORDER BETWEEN THE PHASE
CYCLES IS NOT DETERMINABLE RESULTING POSSIBLY IN COARSE UNWRAPPING ERRORS &IG AND ILLUSTRATE THESE EFFECTS OCCURRING
DUE TO LAYOVER AND TEMPORAL DECORRELATION
&IGURE 7IENER ESTIMATION FOR SPATIAL IMAGE RESTORATION %XPLANATIONS ARE GIVEN IN THE TEXT
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
149
Marc Honikel
-ATHEMATICALLY THIS CORRUPTION IS DESCRIBED IN THE VECTORSPACE MODEL WITH
G "F N
WHERE G IS THE INTERFEROMETRIC PHASE OBSERVATION VECTOR F IS THE VECTOR OF THE IDEAL INTERFEROGRAM AND " IS A MATRIX
WHOSE ELEMENTS ARE POINTS ON THE IMPULSE RESPONSE FUNCTION OFTEN DENOTED AS POINT SPREAD FUNCTION 4HE NOISE N IS
ASSUMED TO BE ZERO MEAN WITH KNOWN COVARIANCE MATRIX +N 0RATT Á
&OR THE RESTORATION OF G AN ESTIMATE F OF THE IDEAL IMAGE F IS SOUGHT WHICH IS GIVEN BY
∧
F 7GB
WHERE 7 IS THE RESTORATION MATRIX AND B IS A BIAS VECTOR 7 AND B ARE CHOSEN FOR 7IENER ESTIMATION IN SUCH A WAY THAT
THEY MINIMIZE THE MEANSQUARE RESTORATION ERROR E WHICH IS DEFINED AS
∧
∧
E %[ F F F F ]
4
-INIMIZATION OF THE LEAST SQUARES RESTORATION ERROR IS ACHIEVED BY APPLYING THE ORTHOGONALITY PRINCIPLE WHICH YIELDS TWO
NECESSARY AND SUFFICIENT CONDITIONS FOR THE DETERMINATION OF 7 AND B
&IRSTLY THE EXPECTATION VALUES OF THE ESTIMATE AND THE IMAGE MUST BE EQUAL
∧
%[ F ] %[ F ]
"Y SUBSTITUTION WITH AND THE BIAS B IS GIVEN BY
B %[ F ]
7%[ G ] %[ F ]
7"%[ F ] 7%[ N ]
3ECONDLY THE RESTORATION ERROR MUST BE ORTHOGONAL TO THE OBSERVATION CENTERED AT ITS MEAN
∧
%[ F F G %[ G ] ] 4
"Y FURTHER SUBSTITUTION AND SIMPLIFICATION THIS YIELDS 0RATT 7 + " "+ " + 4
4
F
F
N
WHERE +F AND +N ARE THE IMAGE AND NOISE COVARIANCE MATRICES
/R BY EXPRESSING +N AND +F BY THEIR ENERGIES sN) AND sF)
7 " "" s s 4
4
N
F
#ERTAIN ASPECTS OF THE FILTER ADAPTATION TO THE VARYING NOISE CAN DIRECTLY BE DERIVED FROM )N CASE THAT THE IMAGE SIGNALTONOISE RATIO REACHES INFINITY IE NO NOISE CORRUPT THE FRINGES THE 7IENER FILTER BEHAVES
EQUIVALENT TO AN INVERSE DECONVOLUTION FILTER WITH
7"
/N THE OTHER HAND IF THE RATIO APPROACHES ZERO 7 BECOMES AND THEREFORE WITH AND ∧
F %[ F ]
FORCING A SMOOTH SOLUTION IN PRESENCE OF EXTREME NOISE
&INALLY IF THE IMAGE SIGNAL IS NOT BLURRED IE " ) 7 BECOMES
7 ) ) s s N
F
INDICATING THE LOWPASS PROPERTIES OF THE FILTERING IN THE SPECIAL CASE OF ONLY ADDITIVE PHASE NOISE
150
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
Marc Honikel
!LTHOUGH 7IENER FILTERING IS THEORETICALLY THE OPTIMAL METHOD FOR THE PHASE DECONVOLUTION IN PRESENCE OF NOISE SEVERAL
PROBLEMS LIMIT ITS EFFECTIVENESS
&IRSTLY THE PRECISE KNOWLEDGE OF THE IDEAL IMAGE F AND THE NOISE TERM N CAN NOT BE ASSUMED FOR MOST APPLICATIONS
INCLUDING THIS ONE -ODELS DEVELOPED FOR THE DIRECT APPROXIMATION OF " ARE TOO WEAK FOR THE HIGHLY COMPLEX PHASE
RESTORATION TASK 3ECONDLY THE ASSUMPTION OF SPATIALLY INVARIANT DEGRADATIONS FOR THE WHOLE IMAGE IS NOT VALID FOR THE
SPATIAL VARIANT INTERFEROMETRIC SIGNATURE 4HIRDLY THE IMAGE AND NOISE SIGNALS ARE ASSUMED TO BE STATIONARY WHICH IS
HARDLY VALID IN MIXED TERRAIN
)N ORDER TO OVERCOME LIMITATIONS TWO AND THREE THE PROPOSED 7IENER FILTERING WILL BE APPLIED LOCALLY DEPENDING ON THE
LOCAL 3.2 4HE DEGRADATIONS BEHAVE SPATIALLY INVARIANT WITHIN THE BORDERS OF A LIMITED WINDOW )N ADDITION THE LOCAL
POWER SPECTRUM WILL HARDLY CHANGE WITHIN THE WINDOW IN COMPARISON TO THE WHOLE INTERFEROGRAM THUS FULFILLING THE
STATIONARITY REQUIREMENT FOR THE 7IENER FILTERING
4HE ABSENCE OF AN IDEAL IMAGE WILL BE OVERCOME IN THIS APPROACH WITH A SYNTHETIC INTERFEROGRAM SIMULATED FROM A
STEREOOPTICAL $%- )T SERVES AS REFERENCE IN THOSE AREAS WHERE THE INTERFEROMETRIC PHASE DETERMINATION FAILS ESPECIALLY
IN LAYOVER AREAS 4HOUGH FAR FROM BEING PERFECT MEASUREMENTS THE SIMULATED DATA WILL DELIVER HERE RELIABLE INFORMATION
AS THE OPTICAL $%- GENERATION IS MUCH LESS ERROR AFFECTED IN STEEP TERRAIN DUE TO THE FACT THAT LAYOVER DOES NOT OCCUR
WITH OPTICAL MEASUREMENTS
2%!,):!4)/. /& 4(% 7)%.%2 0(!3% %34)-!4)/.
&ILTER $EVELOPMENT
"IAS ESTIMATION 4HE LOCAL OFFSET BETWEEN THE INTERFEROMETRIC PHASE MEASUREMENT AND THE SIMULATED PHASES IS
COMPUTED WITH IN A SMALL ESTIMATION WINDOW WHERE BOTH THE CORRELATION COEFFICIENTS OF THE SIMULATED AND THE
INTERFEROMETRIC PHASES ARE MAXIMAL 4HE BIAS ESTIMATION WINDOW IS LOCATED AS NEAR AS POSSIBLE TO THE DEGRADED REGION
INDICATED BY ITS LOW COHERENCE WHICH WOULD SPOIL THE RESULTS IF IT WAS USED FOR BIAS ESTIMATION
)N CASE OF SLIGHTLY DEGRADED MEASUREMENTS THE MATRIX 7 BECOMES CLOSE TO ) AND THEREFORE
B %[ F ]%[ G ]
&OR THE LOCAL FILTERING APPROACH PURSUED HERE THE RESULTING BIAS ESTIMATE CAN BE ASSUMED CONSTANT WITHIN THE WHOLE
RESTORATION WINDOW
2ESTORATION FUNCTION )N ORDER TO AVOID THE HIGH COMPUTATIONAL AND IMPLEMENTATIONAL COST FOR THE NUMERIC
REALIZATION OF IN THE SPATIAL DOMAIN THE VALIDATION OF THE ASSUMPTIONS MADE ABOVE IS FOR THE TIME PERFORMED IN THE
&OURIER DOMAIN WHICH ALLOWS A MUCH FASTER PROCESSING !S THE FILTERING IS RESTRICTED LOCALLY THE RESULTS WILL SUFFER ONLY
LITTLE FROM THE LIMITATIONS OF THE &OURIER DOMAIN PROCESSING !NDREWS REFERS ON THE GENERALIZATION OF THE FILTER
EQUATIONS OF THE VECTORSPACE DOMAIN FROM SECTION TO THE HERE IMPLEMENTED FILTER IN THE &OURIER DOMAIN WHICH HAS
BEEN REALIZED AS A PARAMETERIZED &OURIER 7IENER FILTER WITH THE TRANSFER FUNCTION
7KL "
KL;\"KL\g 0NKL0SKL=
7ITH "KL BEING THE COMPLEX POINT SPREAD FUNCTION AND 0NKL0SKL THE INVERSE OF THE SIGNAL TO NOISE RATIO AND g IS A
FILTER DESIGN CONSTANT WHICH ALLOWS ADDITIONAL CONTROL OVER THE FILTER BEHAVIOR )F g IS SET TO THE FILTER BEHAVES LIKE THE
TRADITIONAL 7IENER FILTER ELSE THE PARAMETER EMPHASIZES g OR DEEMPHASIZES g THE NOISE AND SIGNAL STATISTICS
.OTE THAT ALL TERMS OF ARE EXPRESSED IN THE &OURIER DOMAIN INDICATED WITH THE K AN L PIXEL COORDINATES
%STIMATION OF THE FILTER PARAMETERS
3YNTHETIC INTERFEROGRAM COMPUTATION !S INPUT DATA FOR THE PROPOSED METHOD TWO MEASUREMENTS ARE USED THE
3!2 INTERFEROGRAM AND A STEREOOPTICAL $%- &IRST A 3!2 INTERFEROGRAM &IG HAS TO BE COMPUTED WITH THE
PROCEDURE GIVEN IN DETAIL IN 0RATI 4HE RELATION OF THE TOPOGRAPHIC PHASE COMPONENT Df AND THE TERRAIN ELEVATION H IN SLANT RANGE IS OBTAINED AFTER
COMPENSATION FOR THE FLAT TERRAIN CONTRIBUTION BY
Df £ +H
WHERE + IS A SCALAR DEPENDING ON THE SENSOR AND ORBIT PARAMETERS 0RATI International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
151
Marc Honikel
!PPLYING TO THE OPTICAL $%- POINTS AFTER A SLANT RANGE CONVERSION DERIVES THE SECOND INDEPENDENT INTERFEROMETRIC
DATA SOURCE THE SYNTHETIC INTERFEROGRAM 4HE BASELINE AND SENSOR INFORMATION NECESSARY FOR HEIGHT TO PHASE AND SLANT
RANGE CONVERSION AND IS OBTAINED FROM THE 3!2 SENSOR SPECIFICATION AND EPHEMERIS DATA 4HE RESULT OF THE SIMULATION IS
AN UNWRAPPED PHASE IMAGE IS WRAPPED IN A RANGE BETWEEN p AND p THROUGH A MODULO p OPERATION &IG 3IGNALTONOISE RATIO !S THE 3.2 DECIDES ABOUT THE FILTER BEHAVIOR THE CORRECT DETERMINATION OF THE 3.2 IS
INEVITABLE FOR THE SUCCESSFUL PHASE RESTORATION )N THE )N3!2 CASE DETERMINATION OF THE 3.2 BECOMES A STRAIGHTFORWARD
TASK AS THIS INFORMATION IS DIRECTLY RETRIEVABLE FROM THE INTERFEROMETRIC PROCESSING BY COMPUTING THE LOCAL COHERENCE r
FROM THE COMPLEX 3!2 IMAGES 8 AND 8
r=
%[ 8 ⋅ 8 ]
%[ 8 ⋅ 8 ] %[ 8 ⋅ 8 ]
(IGH COHERENCE INDICATES THOSE AREAS WHERE PHASE ESTIMATION FOR $%- GENERATION IS REASONABLE &IG 4HE 3.2 CAN
BE EXPRESSED AS A FUNCTION OF THE COHERENCE WITH
3.2 =
r
− r
.OTE THAT A COHERENCE ESTIMATE IS COMPUTED WITHIN AN ESTIMATOR WINDOW FROM THE FLATTENED INTERFEROGRAM 3MALL THEREFORE THE ESTIMATED PHASE NOISE DEPENDS ON THE SIZE OF THE ESTIMATOR WINDOW 0RATI 3TILL THE ESTIMATED
COHERENCE IS A VERY GOOD MEASURE FOR THE LOCAL 3.2
0OINT SPREAD FUNCTION 2EFERRING TO &IG "KL RELATES THE IDEAL IMAGE &KL TO THE OUTPUT OF THE BLURRING
'BKL BEFORE THE NOISE ADDITION "OTH THE IDEAL IMAGE F AND THE BLURRING ARE DETERMINED FROM THE GIVEN DATA FOR THE
COMPUTATION OF "KL
4HOUGH THE SIMULATED PHASES MAY GIVE A GOOD APPROXIMATION OF THE IDEAL PHASE COURSE MEASURES HAVE TO BE TAKEN IN
ORDER TO AVOID THE INTRODUCTION OF OPTICAL $%- ERRORS INTO THE INTERFEROMETRIC PROCESSING CHAIN ! WEIGHTING OF THE
SIMULATED PHASES WITH RESPECT TO THEIR EXPECTED ERROR IS PERFORMED USING THEIR CROSSCORRELATION COEFFICIENT ORIGINATING
FROM THE 30/4 IMAGE MATCHING &IG (IGH CROSSCORRELATION INDICATES THE SIMILARITY BETWEEN STEREO IMAGES TO BE
MATCHED AND THEREFORE IS A MEASURE OF RELIABILITY OF THE DETECTION OF CONJUGATE POINTS %RRONEOUS MATCHING STILL OCCURS
EVEN IF THE CORRELATION IS HIGH OFTEN CAUSING SPIKES IE POINTS WITH HIGH HEIGHT DEVIATION COMPARED TO THE SURROUNDING
MEAN 4HESE SPIKES ARE INTERPRETED AS UNCORRELATED RANDOM NOISE IN THE $%- ADDING TO THE LOCAL HEIGHT VARIANCE
4HEREFORE POINTS SHOWING EXTREME HEIGHT VARIANCE ARE EXCLUDED FROM THE PHASE SIMULATION BY GIVING THEM ZERO WEIGHT
)N ORDER TO INCREASE THE NUMBER OF VALID PHASE MEASUREMENTS THUS MINIMIZING HOLES IN THE IDEAL INTERFEROGRAM THROUGH
THE WEIGHTING ALSO HIGHLY COHERENT INTERFEROMETRIC PHASE VALUES r ARE USED IN THE COMPUTATION OF &KL
! BLURRED INTERFEROGRAM IS APPROXIMATED BY PHASE SUBSAMPLING IN AZIMUTH DIRECTION BY FACTOR FOLLOWED BY PHASE
AVERAGING FOR NOISE REDUCTION !LTHOUGH THE RESULTING IMAGE GB HAS A LOWER RESOLUTION THE NOISE LEVEL IS MASSIVELY
REDUCED HENCE IT SERVES FOR THE ESTIMATION OF THE POINT SPREAD FUNCTION WHICH IS FINALLY COMPUTED IN THE &OURIER DOMAIN
BY
"KL ' KL& KL
B
&IGURE %23 DAYPASS
INTERFEROGRAM ^KM
152
&IGURE 0HASE COHERENCE
INDICATES THE NOISE OF &IG &IGURE )NTERFEROGRAM
SIMULATED A 30/4 $%-
&IGURE #ROSS#ORRELATION
FROM THE POINT MATCHING
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
Marc Honikel
&53)/. /& ! 30/4 34%2%/ $%- 7)4( !. %23 ).4%2&%2/'2! 4EST DATA
4HE TEST DATASET CONSISTS OF A PAIR OF %23 3,# QUARTER SCENES &RAME 1UARTER /RBITS AND ACQUIRED IN
A THREE DAY INTERVAL AND AND A 30/4 STEREOPAIR TAKEN IN A FOUR DAY INTERVAL AND "OTH DATA
SETS ARE PART OF A DATA SET OF #ATALONIA USED FOR OUR WORK IN THE %5 PROJECT /2&%!3 0ATIAS 4HE TEST SITE COMPRISES AN AREA OF APPROXIMATELY KM AND SHOWS AN UNDULATING TERRAIN WITH A HEIGHT DIFFERENCE OF
M BETWEEN THE MINIMAL AND MAXIMAL HEIGHT ! $%- IN M GRID DERIVED FROM A TOPOGRAPHIC MAP SERVED
AS REFERENCE FOR OUR COMPUTATIONS 4HE ROOT MEAN SQUARE RMS ERROR OF THE REFERENCE $%- WAS APPROXIMATELY M
4HE DATA HAS BEEN PROCESSED WITH COMMERCIAL SOFTWARE PACKAGES 4HE 30/4 $%- IS PART OF THE $%- OF THE FULL SCENE
WHICH HAS BEEN GENERATED BY THE ,EICA (ELAVA $07 DIGITAL PHOTOGRAMMETRIC WORKSTATION WHICH USES CROSS
CORRELATION FOR MATCHING 4HE CORRELATION COEFFICIENT OF EACH POINT IS NOT ACCESSIBLE DIRECTLY BUT IS HIDDEN BEHIND A
FIGURE OF MERIT &/- 4HIS &/- IS IN A RANGE FROM TO AND IS RELATED TO THE CORRELATION COEFFICIENT ,EICA 4HE 3!2 INTERFEROGRAM AND THE )N3!2 $%- HAVE BEEN GENERATED WITH THE 0#) 6 )&3!2 PACKAGE )&3!2 OFFERS
ALSO THE OPPORTUNITY FOR PHASE SIMULATION FROM A GIVEN $%- "OTH THE ORIGINAL INTERFEROMETRIC MEASUREMENTS AND THE
RESULTS OF THE PHASE RESTORATION ARE UNWRAPPED WITH THE GHOSTLINE ALGORITHM !LTHOUGH THE AVERAGE COHERENCE OF THE
EXAMINED SCENE WAS RELATIVELY HIGH r £ DUE TO THE SHORT REPEAT PASS INTERVAL SEVERAL REGIONS OF LOW COHERENCE
HAVE BEEN OBSERVED AND TREATED WITH THE FILTER
$UE TO LACKING GROUND CONTROL POINTS GCP GCPS HAVE BEEN DERIVED FROM THE REFERENCE $%- FOR GEOCODING AND
BASELINE ESTIMATION IMPROVEMENT "ASELINE FITTING HAS BEEN PERFORMED BY A TECHNIQUE PROPOSED BY 7ERNER 4HE
SIMULATED PHASES HAVE BEEN REGISTERED IN SLANTRANGE TO THE GEOMETRY OF THE INTERFEROGRAM WITH MANUALLY COLLECTED
TIEPOINTS
0HASE RESTORATION
4HE 7IENER FILTERING METHOD HAS BEEN APPLIED TO SEVERAL REGIONS WITHIN THE INTERFEROGRAM WHERE THE PHASE
MEASUREMENT INITIALLY FAILED !S THE PROPOSED METHOD IS SPATIALLY VARIANT PERFORMING LOCAL FILTERING CERTAIN REGIONS OF
INTEREST HAD TO BE FOUND !S STATED ABOVE PHASE RESIDUALS OCCURRING DUE TO NOISE OR LAYOVER EFFECTS ARE LEADING TO PHASE
UNWRAPPING PROBLEMS AND WERE THEREFORE TARGETED BY THE FILTERING 2ESIDUAL REDUCTION AND THE RECONSTRUCTION OF THE
FRINGE BORDER ARE TAKEN AS MEASURES OF QUALITY OF THE PROCEDURE 2ESIDUALS GENERALLY OCCUR IN PRESENCE OF NOISE HENCE
COHERENCE INDICATES THE REGIONS OF INTEREST TO BE TREATED WITH THE 7IENER FILTER 4HE COHERENCE HAS THEREFORE BEEN USED
FOR THE SEGMENTATION OF THE IMAGE IN MORE AND LESS AFFECTED REGIONS 4HE FILTERING HAS BEEN PERFORMED WITHIN A WINDOW
OF SIZE . X - WITH NATURAL NUMBERS . AND - REQUIRED FOR THE &OURIER DOMAIN PROCESSING 4YPICAL VALUES FOR . AND -
HAVE BEEN BETWEEN AND 4HE MEASUREMENT PROBLEMS OCCURRING IN THE INTERFEROGRAM PROVED THE ERROR ASSUMPTION OF THE DEGRADATION MODEL OF
SECTION 4WO MAIN ERROR TYPES HAVE BEEN ENCOUNTERED AND CONSEQUENTLY REMOVED
&RINGE BORDER DEGRADATION
/CCURRING MOSTLY DUE TO ALIASING EFFECTS IT ENDANGERS THE WHOLE HEIGHT DETERMINATION PROCESS FORCING MANUAL TREATMENT
IN FORM OF FRINGE LINE EDITING )N PART THE PROBLEMS IN THESE AREAS HAVE BEEN SO SEVERE THAT EVEN MANUAL EDITING OF FRINGE
LINE WAS NOT POSSIBLE &IG SHOWS AN EXAMPLE OF DEGRADATIONS OF THIS TYPE WHERE RESIDUALS POSITIVE RESIDUALS ARE
GIVEN THE COLOR GREEN NEGATIVE RESIDUALS ARE RED AND THE CORRUPTED FRINGE BORDER YELLOW ARE SHOWN
"Y APPLYING THE 7IENER FILTER TO THESE REGIONS THE AFFECTED FRINGE BORDERS COULD BE RESTORED COMPLETELY !LL OCCURRING
RESIDUALS VANISHED THROUGH THE FILTERING ENABLING SMOOTH PHASE UNWRAPPING EVEN IN THOSE AREAS IN WHICH THE
UNWRAPPING ORIGINALLY FAILED 4HE FRINGE COURSE COULD BE ESTIMATED FOR THOSE AREAS WHERE MANUAL EDITING WAS INITIALLY
NOT POSSIBLE AND HAD BEEN EXCLUDED FROM THE HEIGHT DETERMINATION PROCESS !S AN EXAMPLE THE RESULT OF THE FILTER
OPERATION APPLIED TO &IG IS GIVEN IN &IG ,OCAL NOISE
.OISE OCCURS RANDOMLY WITHIN THE FRINGES DUE TO DECORRELATION OF THE INTERFEROMETRIC PHASES 4HESE PROBLEMS ARE LESS
SEVERE COMPARED TO THE PROBLEMS CAUSED BY THE FRINGE BORDER DEGRADATION AS THEY ARE LOCALLY RESTRICTED 3TILL AS THEY
OCCUR RANDOMLY THEY REQUIRE DETECTION BY THEIR LOW COHERENCE VALUE FOLLOWED BY LOCAL TREATMENT &IG SHOWS A TYPICAL
EXAMPLE OF RANDOM LOCAL NOISE
4HE PHASE FILTERING PERFORMED ALSO WELL WITH THIS TYPE OF DEGENERATION 4HE AFFECTED AREAS HAVE BEEN SMOOTHED
ACCORDING TO THE FILTER BEHAVIOR IN PRESENCE OF ADDITIVE NOISE !DJACENT VALID FRINGE BORDERS HAVE NOT BEEN AFFECTED FROM
THE FILTER OPERATION PROVING THE ABILITY OF THE FILTER TO ADAPT TO THE LOCAL NOISE &IG International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
153
Marc Honikel
&IGURE $EGRADED FRINGE
BORDERS
&IGURE 2ESTORED BORDERS
AFTER THE 7IENER FILTERING
&IGURE 2ANDOM NOISE
OCCURRENCE
&IGURE .OISE REMOVAL BY
FILTERING
)MPROVEMENT OF )N3!2 TOPOGRAPHIC HEIGHT MEASUREMENT
!FTER THE SUCCESSFUL APPLICATION OF THE FILTER TO THE PHASE NOISE REDUCTION PROCESS ITS IMPACT ON THE INTERFEROMETRIC HEIGHT
DETERMINATION HAS BEEN STUDIED ! SUBREGION OF THE SITE OF APPROXIMATELY KM CONTAINING MILLION PHASE
MEASUREMENTS HAS BEEN SELECTED FROM THE %23 DATA SETS FOR THE $%- GENERATION 4HE PHASE UNWRAPPING HAS BEEN
PERFORMED WITH THE GHOSTLINE METHOD &OR THE EVALUATION OF THE FILTERING TWO $%-S ONE WITH AND THE OTHER WITHOUT
7IENER NOISE REDUCTION &IG HAVE BEEN PRODUCED AND COMPARED TO THE 30/4 RESULTS AND THE REFERENCE $%-
4HE 30/4 AND %23 $%-S HAVE BEEN SAMPLED IN A M GRID AND WERE COMPARED TO GROUND TRUTH BY BILINEAR
INTERPOLATION OF EACH HEIGHT VALUE IN THE REFERENCE $%- 4HE RESULTING ERROR STATISTICS IN TERMS OF MEAN RMS AND THE
MAXIMUM ERRORS ARE GIVEN IN 4AB %RROR ;M=
3TEREO/PTICAL
)N3!2
7IENER FILTERED
)N3!2
-EAN
2-3
sEXMIN
sEXMAX
4ABLE %RROR STATISTICS OF THE 30/4 %23 AND FILTERED 3!2OPTICAL $%)N COMPARISON TO THE ORIGINAL INTERFEROMETRIC HEIGHT MEASUREMENTS THE 7IENER ENHANCED )N3!2 $%- SHOWS IMPROVED
STATISTICS IN ALL CATEGORIES 4HE RELATIVELY HIGH MEAN ERROR MAY BE A RESULT OF THE GCP DETERMINATION 4HE DIFFERENCE OF M
FOR THE MEAN BETWEEN THE )N3!2 $%-S INDICATES THE SYSTEMATIC CHANGES DUE TO THE 7IENER FILTERING 4HE 7IENER
)N3!2 $%- IS CONSIDERABLY IMPROVED WITH RESPECT TO THE RMS ERROR WHICH DECREASED BY AND MAXIMUM ERRORS
BOTH BEING FRACTIONS OF THE ORIGINAL ONES
)N3!2 AND STEREOOPTICAL HEIGHT MEASUREMENTS ACHIEVE AN INITIAL RMS ERROR WHICH IS BENEATH THE PIXEL RESOLUTION OF THE
SENSOR 30/4 M %23 M 4HE INITIAL PIXEL RESOLUTION IS A FACT THAT IS HARDLY CONSIDERED WHEN COMPARING THE
)N3!2 WITH STEREOOPTICAL $%-S )N THIS CONTEXT IT IS MOST REMARKABLE THAT THE 7IENER )N3!2 $%- IS SUPERIOR TO THE
30/4 HEIGHT MEASUREMENTS IN RMS AND MAXIMUM ERRORS AGAIN CONSIDERABLY REDUCED .O ERRORS HIGHER THAN
M OCCURRED IN THE IMPROVED )N3!2 $%- WHILE IN THE ORIGINAL )N3!2 $%- AND IN THE 30/4 $%- OF
ALL VALUES SHOWED AN ERROR HIGHER THAN M .ONE OF THE EXTREME CORRUPTED MEASUREMENTS OF THE 30/4 $%- ENTERED
THE FUSION PROCESS DUE TO THE WEIGHTING PROCEDURE
4HESE RESULTS EMPHASIZE THE INTERFEROMETRIC HEIGHT MEASUREMENT CAPABILITIES IN CASE OF RESTORED PHASES )T IS IMPORTANT
TO NOTE THAT THE )N3!2 MEASUREMENTS HAVE BEEN IMPROVED WITH THE SIMULATED PHASES TO AN EXTENT THAT THE QUALITY OF THE
RESULT IS HIGHER THAN THE ASSUMED IDEAL DATA SOURCE
&INALLY THE AMOUNT OF MEASUREMENTS HAS BEEN INCREASED BY THIS METHOD FROM POINTS ORIGINATING FROM THE
30/4 MEASUREMENTS TO MORE THAN POINTS IN THE IMPROVED )N3!2 $%-
#/.#,53)/.3
! NEW METHOD FOR THE FUSION OF OPTICAL AND 3!2 INTERFEROMETRIC DATA BY APPLYING 7IENER FILTERING FOR PHASE RESTORATION
HAS BEEN INTRODUCED AND TESTED )T REDUCES THE EFFECT OF NOISE ON THE INTERFEROMETRIC HEIGHT DETERMINATION NAMELY THE
DEGRADATION OF FRINGE BORDERS TYPICALLY CAUSED BY LAYOVER AND THE OCCURRENCE OF LOCAL PHASE NOISE EG DUE TO
VEGETATION )N THIS WAY NEW INTERFEROMETRIC HEIGHT MEASUREMENTS LIKE FROM 324- CAN BE RELATED TO AND ENHANCED
WITH FORMER PHOTOGRAMMETRIC MEASUREMENTS 4HE PRESENTED PROCEDURE HELPS OVERCOMING THE LIMITATIONS OF THE
INTERFEROMETRIC HEIGHT DETERMINATION BY TAKING ADVANTAGE FROM THE SYNERGY BETWEEN OPTICAL AND 3!2 HEIGHT
MEASUREMENTS IN CRITICAL AREAS 4HE NOISEADAPTIVE DATA FUSION PROCESS PRESERVES VALID INTERFEROMETRIC MEASUREMENTS
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
Marc Honikel
WHILE RESTORING THEM IN CASE OF DEGRADATION )N ORDER TO AVOID THE INTRODUCTION OF CORRUPTED MEASUREMENTS IN THE FUSION
PROCESS AN ATTRIBUTE HAS BEEN DERIVED INDICATING THE EXPECTED ERROR OF THE MEASUREMENT
4HIS LOCAL APPROACH LEADS TO A GLOBAL IMPROVEMENT OF THE RESULTING HEIGHT MEASUREMENTS WITH RESPECT TO
• !MOUNT OF VALID MEASUREMENTS REDUCTION OF MEASUREMENT HOLES
• $%- ERROR DISTRIBUTION
2EDUCTION OF MEAN AND ROOT MEAN SQUARE ERROR
%XTREME REDUCTION OF OUTLIERS
4HE ACHIEVED RESULTS ARE MUCH SUPERIOR COMPARED TO THE INITIAL RESULTS FROM THE SINGLE SENSOR DATA SOURCES AND ENCOURAGE
THE WORK ON A COMPLETE NUMERICAL REALIZATION OF THE 7IENER PHASE ESTIMATION IN THE SPATIAL DOMAIN
&IGURE 2ESTORED INTERFEROGRAM DRAPED OVER THE 7IENER IMPROVED ELEVATION MODEL
2%&%2%.#%3
!NDREWS ( (UNT " $IGITAL )MAGE 2ESTORATION 0RENTICE (ALL )NT .EW *ERSEY PP 'OLDSTEIN 2 :EBKER ( 7ERNER # 3ATELLITE 2ADAR )NTERFEROMETRY 4WO DIMENSIONAL PHASE UNWRAPPING 2ADIO
3CI VOL NO PP (ONIKEL - &USION OF /PTICAL AND 2ADAR $IGITAL %LEVATION -ODELS IN THE 3PATIAL &REQUENCY $OMAIN 0ROC ND
)NT 7ORKSHOP 2ETRIEVAL OF "IO AND 'EOPHYSICAL 0ARAMETERS FROM 3!2 $ATA %34%# .ORDWIJK PP (ONIKEL - $ATA &USION 3TRATEGIES FOR THE &USION OF )N3!2 AND 3TEREO/PTICAL $%-S )NT !RCHIVES OF
0HOTOGRAMMETRY AND 2EMOTE 3ENSING 6OL 0ART 7 PP ,EICA (ELAVA 3/#%4 3%4 7INDOWS .45.)8 5SER -ANUAL 2ELEASE PP &
0RATT 7 + $IGITAL )MAGE 0ROCESSING ND ED *OHN 7ILEY 3ONS .EW 9ORK PP
0ATIAS 0 ED /2&%!3 /PTICAL 2ADAR 3ENSOR &USION FOR %NVIRONMENTAL !PPLICATIONS &INAL %5 0ROJECT 2EPORT
#ONTRACT NO %.6#4
0RATI # 2OCCA & -ONTI'UARNIERI ! 0ASQUALI 0 %23 )NTERFEROMETRIC 4ECHNIQUES AND !PPLICATIONS
)3023 0ROCEEDINGS OF 0RIMARY $ATA !CQUISITION AND %VALUATION PP 3MALL $ 7ERNER # .¼ESCH $ 'EOCODING AND 6ALIDATION OF %23 )N3!2$ERIVED $IGITAL %LEVATION -ODELS
%!23EL !DVANCES IN 2EMOTE 3ENSING 8 PP
7ERNER # 4ECHNIQUES AND !PPLICATIONS OF 3!2 )NTERFEROMETRY FOR %23 4OPOGRAPHIC -APPING #HANGE
$ETECTION AND 3LOPE -EASUREMENT 0ROC ST %23 3YMPOSIUM 3PACE AT THE 3ERVICE OF OUR %NVIRONMENT PP
:EBKER ( 7ERNER # 2OSEN 0 !CCURACY OF 4OPOGRAPHIC -APS $ERIVED FROM %23 )NTERFEROMETRIC 2ADAR
)%%% 4RANSACTIONS ON 'EOSCIENCE AND 2EMOTE 3ENSING PP International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000.
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